Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x+6y &= -8 \\ x+y &= 2\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {-x+2}$ Substitute this expression for $y$ in the first equation. $-6x+6({-x + 2}) = -8$ $-6x - 6x + 12 = -8$ Simplify by combining terms, then solve for $x$ $-12x + 12 = -8$ $-12x = -20$ $x = \dfrac{5}{3}$ Substitute $\dfrac{5}{3}$ for $x$ back into the top equation. $-6( \dfrac{5}{3})+6y = -8$ $-10+6y = -8$ $6y = 2$ $y = \dfrac{1}{3}$ The solution is $\enspace x = \dfrac{5}{3}, \enspace y = \dfrac{1}{3}$.